4.5 cm too little boundary distance - garden wall

At 20 m length, the farmer loses 0.5 sqm. I hardly believe he will be satisfied with €2.50.

Correct. And the calculation shows how absurd a tantrum over 5 cm is. Even if you offered him ten times the land value for an area that belongs to you anyway, he could buy himself a crate of beer with it. So offer him €20 to €50 as an apology, and if he doesn’t want to talk, lean back and wait to see what he will do. There are cases where 5 cm matter, e.g., at a garage yard, if because of an encroachment by the neighbors the prefabricated garage no longer fits into the gap. But with the “Schwengelrecht”? Nobody will seriously deal with the case legally.

There are boundary stakes in the ground.

Made of wood? Doesn’t sound like the boundary line is known to the centimeter. Anything under 6 cm usually falls within the margin of error in the cadastre anyway.
And what damage does the farmer want to quantify? The “Schwengelrecht” is a concession to the farmers. In fact, he has no business on your property. It is just a safety zone for unhindered cultivation of the field.

Your property, your wall... Five centimeters here or there, the farmer can go to hell. Just wait and see what happens....

Your property, your wall... Five centimeters more or less, the farmer can kiss my ass.

Well, however, the OP has violated neighborhood law. The farmer can take legal action against that. Either I comply with legal requirements or I don't.

Just wait and see what happens....

In my opinion, that is the right, pragmatic approach. First, let tempers cool down.

Would wait

He might just be angry because he now has to put in more effort when turning

In my opinion, a new wall is disproportionate. You did not build on his property, you are granting him a few centimeters less right of passage on your property

I would first check whether the Schwengelrecht actually still applies. Here in Saxony, it is like this:

Even better, according to §1 it only applies: "if both properties are located outside a continuously built-up area." So basically, it is sufficient if one of the properties is situated within a settlement area.

The Schwengelrecht is intended in agriculture to prevent very wide but very long - unusable buffer strips from arising between two agriculturally used properties.

But especially with today's technology (GPS), it is possible to approach boundaries with almost centimeter precision without crossing them.

In this case, the law in Baden-Württemberg applies: Are there also these exceptions or loopholes like the mentioned 6cm tolerance there?